Direct relativistic extension of the Schrodinger equation

Recent results obtained by solving the following relativistic equation for a particle with mass m and spin-0 [1-5]:

ih ∂Ψ/∂t = -h²/[(γ_v+1)m] ▽²Ψ + V, γ_v = (1-v²/c²)^-1/2 (1)

are discussed. In Eq. (1), h is the reduced Plank constant, and γ_v depends on the ratio between the particle speed (v) and the speed of the light in the vacuum (c) . Clearly, Eq. (1) coincides with the Schrodinger equation when v² << c². Due to the formal similarity between Eq. (1) and the Schrodinger equation, Eq. (1) can be solved following the same procedures used for solving the Schrodinger equation [1-5]; therefore, Eq. (1) provides a pedagogical approach for introducing the consequences for Quantum Mechanics of the principal ideas of Special Theory of Relativity. Moreover, Eq. (1) allows simpler approaches for a relativistic description of the quantum states of a particle [1-5]. The existing relationship between Eq. (1) and the Dirac, and Klein-Gordon equations are also discussed.
1. L. Grave de Peralta, European Journal of Physics, 41, 065404 (2020).
2. L. Grave de Peralta, Scientific Reports 10, 14925 (2020).
3. L. Grave de Peralta, Results in Physics 18, 103318 (2020).
4. L. Grave de Peralta, Journal of Modern Physics 11, 788 (2020).
5. L. Grave de Peralta, Journal of Modern Physics 11, 196 (2020).